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6-8 Accelerated 7 Unit 1 Lesson 17

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 •Lesson 17 Lesson 18

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Lesson 17

17.1 Warm-up 17.2 Activity 17.3 Activity Student Lesson Summary

Unit 1, Lesson 17

Drawing Triangles (Part 2)

Accelerated 7

17.1

Warm-up

Using a Compass to Estimate Length

Draw a angle.
Use a compass to make sure both sides of your angle have a length of 5 centimeters.
If you connect the ends of the sides you drew to make a triangle, is the third side longer or shorter than 5 centimeters? How can you use a compass to explain your answer?

Are You Ready for More?

17.2

Activity

Revisiting How Many Can You Draw?

Standards Alignment

Building On

Addressing

7.G.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

View Full Standard

Building Toward

Draw as many different triangles as you can with each of these sets of conditions:
1. One angle measures , one side measures 4 cm, and one side measures 5 cm.
2. Two sides measure 6 cm, and one angle measures .
Did either of these sets of measurements determine one unique triangle? How do you know?

17.3

Activity

Three Angles

Standards Alignment

Building On

Addressing

7.G.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

View Full Standard

Building Toward

Draw as many different triangles as you can with each of these sets of measurements:
1. One angle measures , one measures , and one measures .
2. One angle measures , one measures , and one measures .
Did either of these sets of measurements determine one unique triangle? How do you know?

Student Lesson Summary

A triangle has six measures: three side lengths and three angle measures.

If we are given three measures, then sometimes there is no triangle that can be made. For example, there is no triangle with side lengths 1, 2, 5, and there is no triangle with all three angles measuring .

One segment 5 units, a circle radius 1 unit centered at an endpoint, a circle radius 2 centered at the other endpoint.

Four segments, joined end to end, each angle 150 degrees.

Sometimes, only one triangle can be made. By this we mean that any triangle we make will be the same, having the same six measures. For example, if a triangle can be made with three given side lengths, then the corresponding angles will have the same measures. Another example is shown here: an angle measuring between two side lengths of 6 and 8 units. With this information, one unique triangle can be made.

Two angles. First, segments length 6 and 8 meet at a 45 degree angle. Second, segments length 6 and 8 meet at a 45 degree angle, a dotted line connects the other endpoints.

Sometimes, two or more different triangles can be made with three given measures. For example, here are two different triangles that can be made with an angle measuring and side lengths 6 and 8. Notice the angle is not between the given sides.

Two different triangles are shown. Both triangles have sides with length 6 and 8, both triangles have 45 degree angles, but one triangle is bigger than the other.

Three pieces of information about a triangle’s side lengths and angle measures may determine no triangles, one unique triangle, or more than one triangle. It depends on the information.

Glossary

None

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Standards Alignment

Building On

Addressing

7.G.2

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

View Full Standard

Building Toward

Are You Ready for More?

Are You Ready for More?